Brexit will be a "huge burden" to both the U.K. government and parliament, which could render these bodies ineffective at addressing other issues, warned a report by the U.K.-based think tank the Institute for Government (IfG).

The IfG suggests that up to 15 new bills, in addition to the Great Repeal (Brexit) Bill, could be required to secure the U.K.'s future beyond its exit from the European Union. These will be announced at the annual Queen's Speech in May, and could address topics such as agriculture and trade.

The Queen's Speech forms part of the ceremonial start to the parliamentary year and outlines proposed legislation. The IfG's report argues that as roughly 20 bills are outlined in the speech, the predicted high proportion of those to be related to Brexit leaves little room to address other, perhaps domestic, issues.

The IfG also suggests that the legislative upheaval that Brexit is likely to catalyze could lead to the government using different routes to make changes to U.K. law, which could mean that such legal amendments are not subject to parliamentary scrutiny.

"The legislation required for Brexit will leave little parliamentary time for anything else … it will be a challenge for both the government and parliament to do all this while still ensuring full scrutiny and leaving room for the government's domestic policy agenda," Hannah White, IfG director of research, said in a statement.

But Andrew Hood, a lawyer at Dechert specializing in EU law and former legal adviser to previous U.K. Prime Minister David Cameron, told CNBC via telephone that the potential 15 additional bills, "minimizes the cliff-edge fear that people have." Hood added that U.K. parliament only has a "certain bandwidth," meaning that domestic issues could be "put on the backburner," but the significance of Brexit meant that it ought to take priority.

He suggested that new U.K. immigration law could be an area to be foregrounded.

In response to the report, a U.K. government spokesperson said in a statement sent to CNBC that: "We've been clear that where there could be significant change, for example in areas such as customs or immigration, there will be primary legislation." It detailed that: "Parliament will have every opportunity to debate and scrutinize the Great Repeal Bill during its passage."